Numerische Mathematik

, Volume 100, Issue 1, pp 71–89 | Cite as

On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations

  • Volker GrimmEmail author


This paper studies a numerical method for second-order oscillatory differential equations in which high-frequency oscillations are generated by a linear time- and/or solution-dependent part. For constant linear part, it is known that the method allows second-order error bounds independent of the product of the step-size with the frequencies and is therefore a long-time-step method. Most real-world problems are not of that kind and it is important to study more general equations. The analysis in this paper shows that one obtains second-order error bounds even in the case of a time- and/or solution-dependent linear part if the matrix is evaluated at averaged positions.


Differential Equation Mathematical Method General Equation Linear Time Linear Part 
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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Mathematics DepartmentLa Trobe UniversityMelbourneAustralia

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